Obtaining, and manipulating, the prediction equation from a gamm model with smooth terms

Question

I have read similar questions submitted here, and have looked in Wood's 2017 book (Generalized additive models: An introduction with R, 2nd edition) but cannot find an answer to my problem.

To set up the question, consider first a simple linear model:fit<-lm(Y~X+Z). Once I get the coefficients from this simple model (say, Y_hat=2.1+0.9X+3.2Z) then I can get the predicted values that Y would have if I set the coefficient of Z to zero (Y_hat*=2.1+0.9X) and the residuals of Y around this new equation.

Now, imagine that I do a generalized additive model (say, with the gamm function of the mgcv package): fit<-gamm(Y~s(X)+s(Z)). How can I get the coefficients of this GAM in such a way that I can do the same thing as with the simple linear equation; i.e. get the predicted values that Y would have if I set the coefficients associated with the smooth function of Z to zero and then obtain the residuals around this new equation? If I extract the coefficients of a GAM (eg coef(fit$lme)) then I can see the coefficients associated with the intercept and of each of the basis functions, but I don't know how to proceed after that. Thanks for any suggestions.

Answer 1

Given

fit <- gamm(Y ~ s(X) + s(Z))

and assuming Y is where you want to predict...

yhat <- predict(fit$gam, newdata = Y, exclude = "s(Z)")

or

yhat <- predict(fit$gam, newdata = Y, terms = c("(Intercept)", "s(Z)"))

should give you want you want, and where prediction doesn't even consider what the random effects are doing if you use them in such a model.

When doing this exclude/terms thing you need to know the labels for the smooths esp if things get more exotic. Look carefully at how terms are named in the output from summary(fit$gam) for example to see how you need to name terms passed to exclude or terms arguments